Lyapunov-Krasovskii functional for coupled differential-functional equations

This article discusses the Lyapunov-Krasovskii functional approach for the stability problem of coupled differential-functional equations. Such systems include as special cases many types of time-delay systems, including lossless propagation model, some neutral time-delay systems and singular time-delay systems. After the general stability theory, the special case of coupled differential-difference equations is discussed, and the necessity for the existence of quadratic Lyapunov-Krasovskii functional is established. Then the stability conditions for systems with time-varying uncertainty are established based on a quadratic Lyapunov-Krasovskii functional. Discretization is used to render the stability conditions to an LMI form.